Extended depth-of-field biometric system

ABSTRACT

An iris recognition system may include an optical system having an intentional amount of spherical aberration that results in an extended depth of field. A raw image of an iris captured by the optical system may be normalized. In some embodiments, the normalized raw image may be processed to enhance the MTF of the normalized iris image. An iris code may be generated from the normalized raw image or the enhanced normalized raw image. The iris code may be compared to known iris codes to determine if there is a match. In some embodiments, the iris code generated by the normalized iris image may be processed with equalization function before comparison with the known iris codes.

FIELD OF THE INVENTION

The subject disclosure is directed to a biometric identification systemhaving an extended depth-of-field optical system with a designed levelof spherical aberration.

BACKGROUND OF THE INVENTION

Biometric systems such as iris recognition systems may capture an imageof a feature of a person having unique characteristics (e.g., an iris)for various purposes, for example, to confirm the identity of the personbased on the captured image. In the example of iris recognition, anoriginal high-quality image of the iris of a person may be captured byan optical system and converted into an iris code which is stored in adatabase of iris codes associated with a group of people. In order tolater confirm the identity of a user, an image of the user's iris iscaptured, an iris code is generated, and the iris code for the capturediris image is compared to iris codes stored in the database. If the iriscode of the captured iris image exhibits a significant level ofsimilarity with a stored iris code (e.g., the Hamming distance betweenthe captured and stored image is less than a threshold), it can beassumed that the iris of the user is a match with the identityassociated with the stored iris code.

Iris recognition systems may have difficulty capturing iris images of asufficient quality for use in this matching procedure. For example, if aperson is moving it may be difficult to capture a high-quality image ofthe iris. Even if a person is stationary, many optical systems requireprecise positioning of the iris relative to the optical system as aresult of the limited depth of field or focus of the optical system.

An extended depth-of-field (EDOF) (also known as extendeddepth-of-focus) optical system may permit more flexibility in capturinga desired image, since the optical system can capture images having arelatively high quality over a larger distance from the optical system,with some sacrifice in the modulation transfer function (MTF) of thecaptured image. EDOF optical systems may include complicated opticalsystems, for example, including either more than one lens element or anon-circularly symmetric wavefront coding plate arranged in the entrancepupil to impart a complex wavefront shape.

EDOF optical systems used in biometrics such as iris recognition maydigitally enhance captured raw images to compensate for the reduced MTFof images captured with the EDOF optical system. This additional layerof processing may consume a large amount of consuming resources, take anextended period of time, or both. This may result in excessive costs fora biometrics system utilizing EDOF technology, or may compromise theperformance of biometrics systems which need to quickly process andcompare biometric features with stored images (e.g., compare an iriscode from a captured image iris image with a database of stored iriscodes).

The above-described deficiencies of today's biometric solutions aremerely intended to provide an overview of some of the problems ofconventional systems, and are not intended to be exhaustive. Otherproblems with conventional systems and corresponding benefits of thevarious non-limiting embodiments described herein may become furtherapparent upon review of the following description.

SUMMARY OF THE INVENTION

The following presents a simplified summary of the specification toprovide a basic understanding of some aspects of the specification. Thissummary is not an extensive overview of the specification. It isintended to neither identify key or critical elements of thespecification nor delineate any scope particular to any embodiments ofthe specification, or any scope of the claims. Its sole purpose is topresent some concepts of the specification in a simplified form as aprelude to the more detailed description that is presented later.

In various embodiments, a method of processing an extendeddepth-of-field (EDOF) image of an iris at an imaging wavelength λIMcomprises capturing a raw image of the iris, wherein the raw image has areduced modulation transfer function (MTF) based on an optical systemhaving an amount of spherical aberration (SA) of 0.2 λIM≦SA≦2 λIM. Themethod also comprises normalizing the raw image. The method furthercomprises generating an iris code based on the normalized raw image.

In various embodiments, a system for processing an extendeddepth-of-field (EDOF) image of an iris at an imaging wavelength λ_(IM),may comprise an optical system having an amount of spherical aberration(SA) of 0.2λ_(IM)≦SA≦2λ_(IM), the optical system being configured toform on an image sensor a raw image having reduced a modulation transferfunction (MTF) based on the spherical aberration. The system may alsocomprise a controller electrically connected to the image sensor,wherein the controller is configured to capture a raw image of the iris,normalize the raw image, and generate an iris code based on thenormalized raw image.

In addition, various other modifications, alternative embodiments,advantages of the disclosed subject matter, and improvements overconventional monitoring units are described. These and other additionalfeatures of the disclosed subject matter are described in more detailbelow.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features of the present disclosure, its nature andvarious advantages will be more apparent upon consideration of thefollowing detailed description, taken in conjunction with theaccompanying drawings in which:

FIG. 1 depicts an exemplary system diagram of a system for imageacquisition, processing, and identification in accordance with someembodiments of the present disclosure;

FIG. 2 depicts an exemplary biometric device in accordance with someembodiments of the present disclosure;

FIG. 3 depicts an exemplary geometrical representation of an iris imageand normalized iris image in two-dimensional space in accordance withsome embodiments of the present disclosure;

FIG. 4A depicts an exemplary plot of raw MTF, enhanced MTF, and MTF gainfunction as a function of spatial frequency in accordance with someembodiments of the present disclosure;

FIG. 4B depicts an exemplary plot of base wavelet functions forgenerating an iris code represented as a function of spatial frequencyin accordance with some embodiments of the present disclosure;

FIG. 4C depicts an exemplary plot of the base wavelet functions forgenerating an iris code modulated by the gain MTF function, as afunction of spatial frequency, in accordance with some embodiments ofthe present disclosure;

FIG. 4D depicts an exemplary plot of a discrete representation of gaincoefficients associated with the modulated wavelet functions of FIG. 4C,as a function of spatial frequency, in accordance with some embodimentsof the present disclosure;

FIG. 5A depicts an exemplary general organogram of an iris imagecapture, processing, and comparison system in accordance withembodiments of the present disclosure;

FIG. 5B depicts an exemplary general organogram of an iris imagecapture, processing, and comparison system including EDOF image captureand MTF enhancement of the raw image in accordance with embodiments ofthe present disclosure;

FIG. 6A depicts an exemplary plot of the raw and enhanced MTF producedby an EDOF optical system with a lens having spherical aberration, atdifferent spatial frequency ranges, in accordance with some embodimentsof the present disclosure;

FIG. 6B depicts an exemplary plot of the raw and enhanced MTF producedby an EDOF optical system with a lens having spherical aberration, atthe low spatial frequency range of FIG. 6A, in accordance with someembodiments of the present disclosure;

FIG. 7 depicts an exemplary organogram representing four paths P1-P4depicting exemplary sequences for biometric identification from imageacquisition to identification, in accordance with some embodiments ofthe present disclosure;

FIG. 8A depicts an exemplary wavelet function in normalized iris spacein accordance with some embodiments of the present disclosure;

FIG. 8B depicts the spatial spectral distribution of the exemplarywavelet function of FIG. 8A in accordance with some embodiments of thepresent disclosure;

FIG. 9A depicts an exemplary Hamming distance distribution forcomparison of iris codes in accordance with some embodiments of thepresent disclosure;

FIG. 9B depicts exemplary Hamming distance distributions for comparisonof iris codes in accordance with some embodiments of the presentdisclosure; and

FIG. 10 depicts MTF enhancement of a normalized iris image in accordancewith some embodiments of the present disclosure.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Exemplary biometric systems such as iris recognitions systems aredescribed herein for the purposes of illustration and not limitation.For example, one skilled in the art can appreciate that the illustrativeembodiments can have application with respect to other biometric systemsand to other recognition applications such as industrial automationsystems.

Reference is now made in detail to the present exemplary embodiments ofthe disclosure, examples of which are illustrated in the accompanyingdrawings. Whenever possible, like or similar reference numerals are usedthroughout the drawings to refer to like or similar parts. Variousmodifications and alterations may be made to the following exampleswithin the scope of the present disclosure, and aspects of the exemplaryembodiments may be omitted, modified, or combined in different ways toachieve yet further embodiments. Accordingly, the true scope of theinvention is to be understood from the entirety of the presentdisclosure, in view of but not limited to the embodiments describedherein.

Embodiments of the present disclosure describe systems and methods ofacquiring iris images with an EDOF optical systems, such as asingle-lens EDOF system. The single-lens EDOF optical systems may use alens presenting a controlled amount of spherical aberration, forexample, as described in PCT Patent Application PCT/IB2008/001304, filedon Feb. 29, 2008, which is incorporated herein by reference. Thecaptured iris image may be processed to integrate characteristics of theoptical transfer function (OTF) that can be reduced by the symmetricalrevolute MTF (Modulation Transfer Function). An iris code produced fromthe captured image may be compared to stored iris codes. The systems andmethods described herein may be implemented by any suitable hardwareand/or software implementation for use in any suitable device that cancapture and process images, such as security systems, tablet computers,cell phones, smart phones, computers, cameras, mobile iris recognitiondevices, restricted-entry devices, CCTV systems, appliances, vehicles,weapons systems, any other suitable device, or any combination thereof.Moreover, it will be understood that an EDOF system and biometriccomparison system may be used for other biometric applications (e.g.,facial recognition, touchless fingerprint) as well as other capture andrecognition systems, for example, in industrial applications.

A generalized single-lens EDOF optical system is first discussed,followed by exemplary embodiments of single-lens imaging optical systemsfor use in the generalized EDOF optical system. This disclosure willthen address an iris recognition system including an EDOF opticalsystem.

Generalized EDOF System

FIG. 1 is a block diagram of an exemplary embodiment of a single-lensEDOF optical system (“system”) 10 in accordance with the presentdisclosure. System 10 includes an optical axis A1 along which isarranged an imaging optical system 20 that consists of a single lenselement 22 and an aperture stop AS located objectwise of the lenselement at an axial distance DS from an objectwise front lens surfaceS1. Aperture stop AS is “clear” or “open,” meaning that it does notinclude any phase-altering elements, such as phase plates,phase-encoding optical elements or other types of phase-altering means.Although any suitable single-lens optical system may be used inaccordance with the present disclosure, in an embodiment, thesingle-lens optical system may be configured as is described in U.S.Pat. No. 8,594,388, which is incorporated herein by reference. Such asingle-lens optical system may include an aperture stop that is locatedat a position that minimizes comatic aberration, and may be constructedof any suitable materials, such as glass or plastic. In someembodiments, the single lens may be a single, rotationally symmetricoptical component made of a single optical material, for example, as isdescribed in U.S. Pat. No. 8,416,334, which is incorporated by referenceherein. In some embodiments, the single lens may include a sphericalrefractive surface, for example, as is described in U.S. Pat. No.8,488,044, which is incorporated by reference herein, or PCT ApplicationNo. PCT/IB2008/001304, filed on Feb. 29, 2008, which is incorporated byreference herein.

Optical system 20 has a lateral magnification M_(L), an axialmagnification M_(A)=(M_(L))², an object plane OP in an object space OSand an image plane IP in an image space IS. An object OB is shown inobject plane OP and the corresponding image IM formed by optical system20 is shown in image plane IP. Object OB is at an axial object distanceD_(OB) from lens element 22.

Optical system 20 has a depth of field DOF in object space OS over whichthe object OB can be imaged and remain in focus. Likewise, opticalsystem 20 has a corresponding depth of focus DOF′ in image space IS overwhich image IM of object OB remains in focus. Object and image planes OPand IP are thus idealizations of the respective positions of object OBand the corresponding image IM and typically correspond to an optimumobject position and a “best focus” position, respectively. In actuality,these planes can actually fall anywhere within their respective depth offield DOF and depth of focus DOF′, and are typically curved rather thanplanar. The depth of field DOF and depth of focus DOF′ are defined bythe properties of optical system 20, and their interrelationship andimportance in system 10 is discussed more fully below.

System 10 also includes an image sensor 30 that has a photosensitivesurface 32 (e.g., an array of charge-coupled devices) arranged at imageplane IP so as receive and detect image IM, which is also referred toherein as an “initial” or a “raw” image. Although any suitable imagesensor 30 may be used in accordance with the present disclosure, in anexemplary embodiment image sensor 30 may be or include a high-definitionCCD camera or CMOS camera. In an exemplary embodiment, photosensitivesurface 32 is made up of 3000×2208 pixels, with a pixel size of 3.5microns. The full-well capacity is reduced to 21,000 electrons for aCMOS camera at this small pixel size, which translates into a minimum ofshot noise of 43.2 dB at saturation level. An example image sensor 30 isor includes a camera from Pixelink PL-A781 having 3000×2208 pixelslinked by IEEE 1394 Fire Wire to an image processor (discussed below),and the application calls API provided by a Pixelink library in a DLL tocontrol the camera perform image acquisition. An example image sensor 30has about a 6 mm diagonal measurement of photosensitive surface 32.

In an exemplary embodiment, system 10 further includes a controller 50,such as a computer or like machine, that is adapted (e.g., viainstructions such as software embodied in a computer-readable ormachine-readable medium) to control the operation of the variouscomponents of the system. Controller 50 is configured to control theoperation of system 10 and includes an image processing unit (“imageprocessor”) 54 electrically connected to image sensor 30 and adapted toreceive and process digitized raw image signals SRI therefrom and formprocessed image signals SPI, as described in greater detail below.

FIG. 2 is a schematic diagram of an exemplary hand-held device 52 thatincludes system 10, in accordance with some embodiments of the presentdisclosure. In an exemplary embodiment, controller 50 is or includes acomputer with a processor (e.g., image processor 54) and includes anoperating system such as Microsoft WINDOWS or LINUX.

In an exemplary embodiment, image processor 54 may be or include anysuitable processor having processing capability necessary to perform theprocessing functions described herein, including but not limited tohardware logic, computer readable instructions running on a processor,or any combination thereof. In some embodiments, the processor mayinclude a general- or special-purpose microprocessor, finite statemachine, controller, computer, central-processing unit (CPU),field-programmable gate array (FPGA), or digital signal processor. In anexemplary embodiment, the processor is an Intel 17, XEON or PENTIUMprocessor, or an AMD TURION or other processor in the line of suchprocessors made by AMD Corp., Intel Corp., or other semiconductorprocessor manufacturers. Image processor 54 may run software to performthe operations described herein, including software accessed in machinereadable form on a tangible non-transitory computer readable storagemedium, as well as software that describes the configuration of hardwaresuch as hardware description language (HDL) software used for designingchips.

Controller 50 may also include a memory unit (“memory”) 110 operablycoupled to image processor 54, on which may be stored a series ofinstructions executable by image processor 54. As used herein, the term“memory” refers to any tangible (or non-transitory) storage mediuminclude disks, thumb drives, and memory, etc., but does not includepropagated signals. Tangible computer readable storage medium includevolatile and non-volatile, removable and non-removable media, such ascomputer readable instructions, data structures, program modules orother data. Examples of such media include RAM, ROM, EPROM, EEPROM,flash memory, CD-ROM, DVD, disks or optical storage, magnetic storage,or any other non-transitory medium that stores information that isaccessed by a processor or computing device. In an exemplary embodiment,controller 50 may include a port or drive 120 adapted to accommodate aremovable processor-readable medium 116, such as CD-ROM, DVD, memorystick or like storage medium.

The EDOF methods of the present disclosure may be implemented in variousembodiments in a machine-readable medium (e.g., memory 110) comprisingmachine readable instructions (e.g., computer programs and/or softwaremodules) for causing controller 50 to perform the methods and thecontrolling operations for operating system 10. In an exemplaryembodiment, the computer programs run on image processor 54 out ofmemory 110, and may be transferred to main memory from permanent storagevia disk drive or port 120 when stored on removable media 116, or via awired or wireless network connection when stored outside of controller50, or via other types of computer or machine-readable media from whichit can be read and utilized.

The computer programs and/or software modules may comprise multiplemodules or objects to perform the various methods of the presentdisclosure, and control the operation and function of the variouscomponents in system 10. The type of computer programming languages usedfor the code may vary between procedural code-type languages toobject-oriented languages. The files or objects need not have a one toone correspondence to the modules or method steps described depending onthe desires of the programmer. Further, the method and apparatus maycomprise combinations of software, hardware and firmware. Firmware canbe downloaded into image processor 54 for implementing the variousexemplary embodiments of the disclosure.

Controller 50 may also include a display 130, which may be any suitabledisplay for displaying information in any suitable manner, for example,using a wide variety of alphanumeric and graphical representations. Insome embodiments, display 130 may display enhanced images (e.g., imagescaptured and enhanced by system 10). Controller 50 may also include adata-entry device 132. Data entry device 132 may include any suitabledevice that allows a user of system 10 to interact with controller 50.For example, a keyboard or touchscreen may allow a user to inputinformation for controller 50 (e.g., the name of the object beingimaged, etc.) and to manually control the operation of system 10. In anexemplary embodiment, controller 50 is made sufficiently compact to fitwithin a small form-factor housing of a hand-held or portable device,such as device 52 shown in FIG. 2.

System 10 may also include a database unit 90 operably connected tocontroller 50. In an embodiment, database unit 90 may include memoryunit 92 that serves as a computer-readable medium adapted to receiveprocessed image signals SPI from image processor 54 and store theassociated processed digital images of object OB as represented by theprocessed image signals. Memory unit 92 may include any suitable memoryas described herein, and may be operably connected to controller 50 inany suitable manner (e.g., locally within system 10 or remotely). In anexemplary embodiment, database unit 90 is included within controller 50.

General Method of Operation

With reference to FIG. 1, in the general operation of system 10, imageIM of object OB is formed on photosensitive surface 32 of sensor 30 byoptical system 20. Controller 50 sends a control signal S30 to activateimage sensor 30 for a given exposure time so that image IM is capturedby photosensitive surface 32. Image sensor 30 digitizes this “raw” imageIM and creates the electronic raw image signal SRI representative of theraw captured image.

Image processor 54 may be adapted to receive from image sensor 30digitized electrical raw image signals SRI and collect the correspondingraw images to be stored in compressed format. The data format can followusual standards such as ISO INCITS 379 and ISO 19794-6. The images canbe stored as native or compressed images (TIFF, bmp, jpeg). In someembodiments, the raw images may be processed further, with the processedversion(s) of the image being stored instead of or in addition to theraw image. For example, as described herein, in some embodiments the rawimage may be enhanced to improve the captured MTF (e.g., for imagescaptured by a system having EDOF optics). In some embodiments such asiris recognition, the images can be processed further to be normalizedand/or to generate a compressed iris code that is specifically stored ina highly compressed format that represents the iris pattern only.

In some embodiments, the raw image IM can be used directly, i.e.,without any processing to enhance the image, or with only minor imageprocessing that does not involve MTF-enhancement, as discussed below.This approach can be used for certain types of imaging applications,such as character recognition and for imaging binary objects (e.g.,bar-code objects) where, for example, determining edge location is moreimportant than image contrast. The raw image IM is associated with anEDOF provided by optical system 20 even without additionalcontrast-enhancing image processing, so that in some exemplaryembodiments, system 10 need not utilize some or all of theimage-processing capabilities of the system. In some embodiments, asdescribed herein, some aspects of processing for iris recognition may beomitted for images captured with an EDOF system and processed.

In an embodiment, a number N of raw images are collected and averaged(e.g., using image processor 54) in order to form a (digitized) rawimage IM′ that has reduced noise as compared to any one of the N rawimages.

In some embodiments, it may be desired enhance the raw image IM. Imageprocessor 54 may receive and digitally process the electronic raw imagesignal SRI to form a corresponding contrast-enhanced image embodied inan electronic processed image signal SPI, which is optionally stored indatabase unit 90.

In some embodiments such as biometric applications, system 10 maycompare captured biometric information (e.g., iris codes associated witha captured iris image and stored in database 90) with known biometricinformation (e.g., iris codes associated with known users and stored indatabase 90 or remotely). Controller 50 may access the stored processedimages or related data (e.g., iris codes) from database unit 90 forcomparison, as described herein. In an exemplary embodiment of irisrecognition, compressed data from normalized iris images may be used forcomparison. In some embodiments, this high end compressed data can fitin small files or data block of 5 kB to 10 kB.

Optical System

As discussed above, imaging optical system 20 has a depth of field DOFin object space OS and a depth of focus DOF′ in image space IS asdefined by the particular design of the optical system. The depth offield DOF and the depth of focus DOF′ for conventional optical systemscan be ascertained by measuring the evolution of the Point SpreadFunction (PSF) through focus, and can be established by specifying anamount of loss in resolution R that is deemed acceptable for a givenapplication. The “circle of least confusion” is often taken as theparameter that defines the limit of the depth of focus DOF′.

In the present disclosure, both the depth of field DOF and the depth offocus DOF′ are extended by providing optical system 20 with an amount ofspherical aberration (SA). In an exemplary embodiment, 0.2λ≦SA≦5λ, morepreferably 0.2λ≦SA≦2λ, and even more preferably 0.5λSA≦1λ, where λ is animaging wavelength. In an exemplary embodiment, the amount of sphericalaberration SA in the optical system at the imaging wavelength λ is suchthat the depth of field DOF or the depth of focus DOF′ increases by anamount between 50% and 500% as compared to a diffraction limited opticalsystem. By adding select amounts of spherical aberration SA, the amountof increase in the depth of field DOF can be controlled. The exampleoptical system designs set forth herein add select amounts of sphericalaberration SA to increase the depth of field DOF without substantiallyincreasing the adverse impact of other aberrations on image formation.

Since the depth of field DOF and the depth of focus DOF′ are related bythe axial magnification M_(A) and lateral magnification M_(L) of opticalsystem 20 via the relationships DOF′=(M_(A)) DOF=(M_(L))² DOF, system 10is said to have an “extended depth of field” for the sake ofconvenience. One skilled in the art will recognize that this expressionalso implies that system 10 has an “extended depth of focus” as well.Thus, either the depth of field DOF or the depth of focus DOF′ isreferred to below, depending on the context of the discussion.

The MTF can also be used in conjunction with the PSF to characterize thedepth of focus DOF′ by examining the resolution R and image contrast CIof the image through focus. Here, the image contrast is given byCI=(I _(MAX) −I _(MIN))/(I _(MAX) +I _(MIN))and is measured for an image of a set of sinusoidal line-space pairshaving a particular spatial frequency, where I_(MAX) and I_(MIN) are themaximum and minimum image intensities, respectively. The “best focus” isdefined as the image position where the MTF is maximized and where thePSF is the narrowest. When an optical system is free from aberrations(i.e., is diffraction limited), the best focus based on the MTFcoincides with the best focus based on the PSF. However, whenaberrations are present in an optical system, the best focus positionsbased on the MTF and PSF can differ.

Conventional lens design principles call for designing an optical systemin a manner that seeks to eliminate all aberrations, or to at leastbalance them to minimize their effect so that the optical system on thewhole is substantially free of aberrations. However, in the presentdisclosure, optical system 20 is intentionally designed to havespherical aberration as a dominant aberration, and may also have a smallamount of chromatic aberration as well.

The spherical aberration reduces the contrast of the image by reducingthe overall level of the MTF from the base frequency f₀=0 to the cutofffrequency f_(C). The cut off frequency f_(C) is not significantlyreduced as compared to the ideal (i.e., diffraction-limited) MTF, sonearly all the original spatial-frequency spectrum is available. Thus,the spatial-frequency information is still available in the image,albeit with a lower contrast. In some embodiments, the reduced contrastmay be restored by the MTF enhancement digital filtering process ascarried out by image processing unit 54, as described below. In someembodiments, it may not be necessary to perform the MTF enhancement,i.e., an EDOF image with a reduced MTF may be used without MTFenhancement, for example, in some embodiments of iris recognition asdescribed herein.

The amount of spherical aberration SA increases the depth of focus DOF′in the sense that the high spatial frequencies stay available over agreater range of defocus. The processing of the image described hereinpermits the image to be used for applications such as biometrics (e.g.,with or without digital filtering that restores the contrast over theenhanced depth of focus DOF′), thereby effectively enhancing the imagingperformance of optical system 20.

Spherical aberration is an “even” aberration in the sense that thewavefront “error” is an even power of the normalized pupil coordinate ρ.Thus, spherical aberration presents a rotationally symmetric wavefrontso that the phase is zero. This means that the resulting OpticalTransfer Function (OTF) (which is the Fourier Transform of the PSF) is arotationally symmetric, real function. The MTF, which is the magnitudeof the OTF, can be obtained where spherical aberration is the dominantaberration by considering a one-dimensional MTF measurement taken on aslanted edge. This measurement provides all the required information torestore the two-dimensional image via digital signal processing. Also,the phase is zero at any defocus position, which allows for digitalimage processing to enhance the MTF without the need to consider thephase component (i.e., the phase transfer function, or PFT) of the OTFin the Fourier (i.e., spatial-frequency) space.

An amount of spherical aberration SA of about 0.75λ gives a significantDOF enhancement without forming a zero in the MTF on one defocus side.Beyond about SA=0.75λ, a zero occurs on both sides of defocus from thebest focus position. For a diffraction-limited optical system, the depthof focus DOF′ is given by the relationship DOF′=±λ/(NA²), where NA isthe numerical aperture of the optical system. In an exemplaryembodiment, optical system 20 has an NA between about 0.033 and 0.125(i.e., about F/15 to about F/4, where F/#=1/(2NA) assuming thesmall-angle approximation).

By way of example, for F/6.6, a center wavelength of λ=800 nm and abandwidth of Δλ, the diffraction-limited depth of focus DOF′ is about 20mm, with a transverse magnification of 1/1.4. The introduction of anamount of spherical aberration SA=0.75λ increases the depth of focusDOF′ to about 100 mm, an increase of about 5×.

MTF Enhancement

In some embodiments, it may be desired to improve the contrast of a rawimage captured with an EDOF system having spherical aberration. In someembodiments, this may be accomplished by filtering the raw images in amanner that restores the MTF as a smooth function that decreasescontinuously with spatial frequency and that preferably avoidsovershoots, ringing and other image artifacts.

Noise amplification is often a problem in any filtering process thatseeks to sharpen a signal (e.g., enhance contrast in a digital opticalimage). Accordingly, in an exemplary embodiment, an optimized gainfunction (similar to Wiener's filter) that takes in account the powerspectrum of noise is applied to reduce noise amplification during thecontrast-enhancement process.

In an exemplary embodiment, the gain function applied to the “raw” MTFto form the “output” or “enhanced” MTF (referred to herein as “outputMTF”) depends on the object distance D_(OB). The MTF versus distanceD_(OB) is acquired by a calibration process wherein the MTF is measuredin the expected depth of field DOF by sampling using defocus stepsδ_(F)≦(⅛)(λ/(NA²) to avoid any undersampling and thus the loss ofthrough-focus information for the MTF. In this instance, the enhancedMTF is said to be “focus-dependent.”

In an embodiment, the MTF gain function may not depend on the objectdistance. Although an MTF gain function may be determined in anysuitable manner, in an embodiment the MTF gain function may be estimatedbased on the ratio of an enhanced MTF target function over the averageof the raw MTF within the allocated depth of field. For example, becausethe typical smooth shape of a desired MTF compared to the MTF of animage acquired by a system having spherical aberration may be known, anapproximation may be sufficiently accurate for MTF enhancement.

The above-mentioned MTF gain function used to restore or enhance the rawMTF is a three-dimensional function G(u, v, d), wherein u is the spatialfrequency along the X axis, v is the spatial frequency along the Y axis,and d is the distance of the object in the allowed extended depth offield DOF (d thus corresponds to the object distance D_(OB)). Therotational symmetry of the PSF and MTF results in a simplifieddefinition of the gain function, namely:G′(ω,d) with ω² =u ² +v ²

The rotational symmetry also makes G′(ω, d) a real function instead of acomplex function in the general case.

The “enhanced” or “restored” OTF is denoted OTF′ and is defined as:OTF′(u,v,d)=G(u,v,d)OTF(u,v,d)where OTF is the Optical Transfer Function of the optical system forincoherent light, OTF′ is the equivalent OTF of the optical systemincluding the digital processing, and G is the aforementioned MTF gainfunction. The relationship for the restored or “output” or “enhanced”MTF (i.e., MTF′) based on the original or unrestored MTF is given by:MTF′(ω,d)=G′(ω,d)MTF(ω,d)

When the object distance is unknown, an optimized average gain functionG′ can be used. The resulting MTF is enhanced, but is not a function ofthe object distance.

The after-digital process may be optimized to deliver substantially thesame MTF at any distance in the range of the working depth of field DOF.This provides a substantially constant image quality, independent ofobject distance D_(OB), so long as D_(OB) is within the depth of fieldDOF of optical system 20. Because optical system 20 has an extendeddepth of field DOF due to the presence of spherical aberration asdescribed below, system 10 can accommodate a relatively large variationin object distance D_(OB) and still be able to capture suitable images.

FIG. 4A depicts an exemplary plot of raw MTF, enhanced MTF, and MTF gainfunction as a function of spatial frequency in accordance with someembodiments of the present disclosure. In an embodiment, these plots mayprovide an exemplary gain function and their corresponding polychromaticprocessed (output) EMTF obtained using the above-described process. TheMTF gain function MGF may be simplified as a frequency function composedof the product of a parabolic function multiplied by a hypergaussianfunction, namely:

${Gain} = {\left( {1 + {A \cdot f^{2}}} \right) \cdot {\mathbb{e}}^{- {(\frac{f^{2}}{f_{0}^{2}})}^{n}}}$

Here, A is a constant, n is the hypergaussian order, and f₀ is thecutoff frequency, which is set at the highest frequency where the rawMTF is recommended to be higher than 5% on the whole range of theextended depth of field DOF. The parameters A, f₀ and n allow forchanging the output MTF′ level and managing the cut off frequencydepending on the Nyquist frequency f_(N) of the image sensor. Reducingthe MTF at the Nyquist frequency f_(N) reduces the noise level andavoids aliasing artifacts in the image.

Although it will be understood that the MGF may be implemented in anysuitable manner, for example, based on the methodology used to obtainthe MGF, in an embodiment one efficient methodology of implementing theMGF may be as a sampled table of calibrated data that may be stored inmemory of system 10.

FIG. 6A depicts an exemplary plot of the raw and enhanced MTF producedby an EDOF optical system with a lens having spherical aberration, atdifferent spatial frequency ranges, in accordance with some embodimentsof the present disclosure, while FIG. 6B depicts an exemplary plot ofthe raw and enhanced MTF produced by an EDOF optical system with a lenshaving spherical aberration, at the low spatial frequency range of FIG.6A, in accordance with some embodiments of the present disclosure. InFIG. 6A, the shape of the output MTF′ is as close as possible to thehypergaussian function, namely:

${{Gain}(f)} = \frac{{\mathbb{e}}^{- {(\frac{f^{2}}{f_{0}^{2}})}^{n}}}{{MTF}_{Z = 0}(f)}$

In this way, the gain function is adapted to produce the hypergaussianoutput MTF′ as described after digital processing. The raw MTFmultiplied by the gain function produces the hypergaussian output MTF′.

The output MTF′ may be represented by a hypergaussian output function.The hypergaussian output MTF′ has some valuable properties of producinga high contrast at low and medium spatial frequencies up to the half cutoff frequency, and may produce a continuous and regular drop thatminimizes overshoot and ringing on the processed PSF, LSF (Line SpreadFunction) and ESF (Edge Spread Function).

If n=1, the output MTF′ is Gaussian. This provides a PSF, LSF and ESFwithout any ringing or overshoot. If n>1, the output MTF′ ishypergaussian. For higher values of n, the contrast at high spatialfrequencies is also high, but ringing and overshoot increases. In someembodiments, a good compromise may be 1>n>2, wherein the output MTF′ iswell enhanced at low and medium spatial frequencies, while the ringingand overshoot are limited to about 5%, which may be acceptable for mostimaging applications. In an exemplary embodiment, the real output MTF′is as close as possible to a hypergaussian.

In some embodiments, it may be desirable to control the power noiseamplification. At distances where the gain on the raw MTF is higher inorder to achieve the output MTF′, a good compromise between the MTFlevel and the signal-to-noise ratio on the image can be determined,while controlling the slope of the output MTF′ at high specialfrequencies may avoid significant overshoot.

In the MTF plots of FIG. 4A, the output MTF “EMTF” has a smooth shapethat avoids overshoots and other imaging artifacts. The applied gain ofthe digital filter is optimized or enhanced to obtain the maximum outputMTF′ while controlling the gain or noise.

Image Noise Reduction by Averaging Sequential Images

There are two distinct sources of noise associated with the imageacquisition and image processing steps. The first source of noise iscalled “fixed-pattern noise” or FP noise for short. The FP noise isreduced by a specific calibration of image sensor 30 at the givenoperating conditions. In an exemplary embodiment, FP noise is reducedvia a multi-level mapping of the fixed pattern noise wherein each pixelis corrected by a calibration table, e.g., a lookup table that has thecorrection values. This requires an individual calibration of each imagesensor and calibration data storage in a calibration file. The mappingof the fixed pattern noise for a given image sensor is performed, forexample, by imaging a pure white image (e.g., from an integratingsphere) and measuring the variation in the acquired raw digital image.

The other source of noise is shot noise, which is random noise. The shotnoise is produced in electronic devices by the Poisson statisticsassociated with the movement of electrons. Shot noise also arises whenconverting photons to electrons via the photo-electric effect.

Some imaging applications, such as iris recognition, require ahigh-definition image sensor 30. To this end, in an exemplaryembodiment, image sensor 30 is or includes a CMOS or CCD camera havingan array of 3000×2208 pixels with a pixel size of 3.5 μm. The full wellcapacity is reduced to 21,000 electrons for a CMOS camera at this smallpixel size, and the associated minimum of shot noise is about 43.2 dB atthe saturation level.

An exemplary embodiment of system 10 has reduced noise so that the MTFquality is improved, which leads to improved images. The random natureof the shot noise is such that averaging N captured images is the onlyavailable approach to reducing the noise (i.e., improving the SNR). Thenoise decreases (i.e., the SNR increases) in proportion to N^(1/2). Thisaveraging process can be applied to raw images as well as to processed(i.e., contrast-enhanced) images.

Averaging N captured images is a suitable noise reduction approach solong as the images being averaged are of a fixed object or scene.However, such averaging is problematic when the object moves. In anexemplary embodiment, the movement of object OB is tracked andaccurately measured, and the averaging process for reducing noise isemployed by accounting for and compensating for the objection motionprior to averaging the raw images.

In an exemplary embodiment, the image averaging process of the presentdisclosure uses a correlation function between the sequential images ata common region of interest. The relative two-dimensional image shiftsare determined by the location of the correlation peak. The correlationfunction is processed in the Fourier domain to speed the calculation byusing a fast-Fourier transform (FFT) algorithm. The correlation functionprovided is sampled at the same sampling intervals as the initialimages. The detection of the correlation maximum is accurate to the sizeof one pixel.

An improvement of this measurement technique is to use a 3×3 kernel ofpixels centered on the pixel associated with the maximum correlationpeak. The sub-pixel location is determined by fitting to two-dimensionalparabolic functions to establish a maximum. The (X,Y) image shift isthen determined. The images are re-sampled at their shifted locations.If the decimal part of the measured (X,Y) shift is not equal to 0, abi-linear interpolation is performed. It is also possible to use aShannon interpolation as well because there is no signal in the image atfrequencies higher than the Nyquist frequency. All the images are thensummed after being re-sampled, taking in account the (X,Y) shift in themeasured correlation.

Iris Image Processing

FIG. 5A depicts an exemplary general organogram of an iris imagecapture, processing, and comparison system including in accordance withembodiments of the present disclosure, while FIG. 5B depicts anexemplary general organogram of an iris image capture, processing, andcomparison system including EDOF image capture and MTF enhancement inaccordance with embodiments of the present disclosure.

In both FIGS. 5A and 5B, a raw image may be acquired by an image sensor30. An exemplary lens and camera system may include settings that passspatial frequencies from 0 to 10 lp/mm in the object space. Amagnification relationship may exist between the object where an iris islocated and the image space where the iris image is formed on an imagecapture device 30. It will be understood that focal length of a lens ofthe system 10 may be determined in any suitable manner, for example, toform the image according to the object distance, resulting in anappropriate pixel size and number of pixels, (e.g., for an image of aniris having a diameter of 10 mm, a range of 150-200 pixels per line).

As noted above, FIG. 5A generally depicts the operation of a system thatdoes not include EDOF optics and processing, and thus, the raw image maybe a high quality image that has MTF characteristics that do not requireenhancement. However, in FIG. 5B the raw image may be captured with EDOFoptics, which may provide advantages as far as the depth of field ofimage capture but may result in an image having reduced MTFcharacteristics. Thus, in FIG. 5B, at step 61 it may be desired toenhance the captured raw image captured by an EDOF system. Although itwill be understood that the raw image may be enhanced in any suitablemanner, in an embodiment the raw image may be enhanced using the MTFenhancement methods described above.

In some embodiments, the raw image of FIG. 5A or the MTF enhanced imageof FIG. 5B may be stored for later use. Although an image may be storedin any suitable manner in any suitable medium, in an embodiment the irisimage may be stored as part of an iris recognition enrollment processand may be stored in an iris enrollment database (e.g., database 90 ofsystem 10, a remote database, and/or any other suitable database). Insome embodiments the iris image may itself be used for iris recognition,such that the acquired iris image is compared to a stored iris imageaccessed from the database.

At step 62 of FIG. 5A or 5B, image processor 54 of system 10 maynormalize the iris image. A typical captured iris image, such as animage complying with ISO INCITS 379 and ISO 19794-6, having a VGA size(640×480 pixels), may typically require 30 kB to 100 kB depending on thecompression level of the image format (e.g., jpeg, jpeg2000, etc.) usedfor the image. For example, a raw 8 bit uncompressed image may require307,200 bytes. As will be described below, for iris recognitionapplications the image may eventually be used to generate an iris codethat is compared to an iris code corresponding to previously stored irisimages of known users.

A raw iris image may include areas around the iris that do not provideuseful information for generation of this iris code. Thus, at step 62the iris image may be normalized.

FIG. 3 depicts an exemplary geometrical representation of an iris imageand normalized iris image in two-dimensional space in accordance withsome embodiments of the present disclosure. Although iris imagenormalization may be performed in any suitable manner, in an embodimentthe normalized image may be generated as a rectangular function usingdata from the iris region of interest representing no more than 8% ofthe whole captured image. In an embodiment, an estimation may be madebased on a 200 pixels across the iris image on a 620×480 pixels area.For embodiments involving a high-resolution camera (e.g., a 5.5 MP or 10MP camera), this ROI area can represent less than 1% of the acquiredimage, for example, of an image of the whole face of a user includingthe two eyes.

The normalized image may have a greatly reduced size in comparison tothe iris image, e.g., less than 10 kB. During normalization, numerousareas not including relevant information for iris recognition may beremoved. In an embodiment, the relevant iris image may be bounded by theinternal pupil boundary 43 and the external iris boundary 41. Otheraspects of the image within the iris boundary that are not relevant toiris recognition may also be removed from the image, including thesclera and the eyelid regions 44 and eyelashes 45. The result of thenormalization process may be a normalised image 46, developed as a polarfunction of θ and radius r on the iris image of FIG. 3.

Returning to FIGS. 5A and 5B, in some embodiments, the normalized imagemay be stored for later use. Although the normalized image may be storedin any suitable manner and in any suitable medium, in an embodiment thenormalized image may be stored as part of an iris recognition enrollmentprocess and may be stored in an iris enrollment database (e.g., database90 of system 10, a remote database, and/or any other suitable database).In some embodiments the normalized image may itself be used for irisrecognition, such that the acquired and normalized image is compared toa stored normalized image accessed from the database.

At step 63, the normalized iris image may be encoded to generate an iriscode for the iris of the acquired image. Iris recognition algorithms maybuild and use identification codes (iris codes) from captured images tobe compared to stored iris codes or to generate the initial iris codeduring an enrollment process. A match between an iris code captured by asystem 10 and a stored iris code from an image captured during aprevious enrollment process may be determined based on a Hammingdistance between the two iris codes, as described herein.

Although it will be understood that the iris code may be generated fromthe normalized image in any suitable manner, in an embodiment amathematical transform may be used to generate the iris code. A commoncharacteristic of these mathematical transforms may be to project thenormalized iris image into a base or vector wavelet and generate a tableof coefficients corresponding to the list of vectors, where each ofthese vectors has a typical print in the frequency domain whenever thistransform is linear or not. Although it will be understood that anysuitable mathematical transform may be used, in an embodiment themathematical transform may be a Gabor transform or a Log Gabortransform. For example, the Gabor Transform (e.g., a discrete GaborTransform) may be adapted to a numerical code to provide a list ofvectors. The discrete Gabor Transform in 2D can be defined by:

${G_{n_{x},n_{y},m_{x},m_{y}}\left( {u,v} \right)} = {\sum\limits_{m_{x} = 0}^{M_{x} - 1}{\sum\limits_{n_{x} = 0}^{N_{x} - 1}{\sum\limits_{m_{y} = 0}^{M_{y} - 1}{\sum\limits_{n_{y} = 0}^{M_{y} - 1}{C_{m_{x},n_{x},m_{y},n_{y}} \cdot {g_{m_{x},n_{x},m_{y},n_{y}}\left( {u,v} \right)}}}}}}$where:

g_(m) _(x) _(,n) _(x) _(m) _(y) _(n) _(y) are the discrete Gaborfunctions

C_(m) _(x) _(,n) _(x) _(,m) _(y) _(,n) _(y) are the coefficients for theidentification code of the iris.g _(m) _(x) _(,n) _(x) _(,m) _(y) _(,n) _(y) =S(u−m _(x) N)·S(v−m _(y)N)·e ^(iΩ) ^(x) ^(m) ^(x) ^(u) ·e ^(iΩ) ^(y) ^(m) ^(y) ^(v)where:

m_(x), n_(x), m_(y), n_(y) are the discrete integer index of Gaborfunctions

S ( ) represents the discrete Gabor functions

u is the index position in the normalized image on the θ axis

v is the index position in the normalized image on the r axis

m_(x) is the discrete order on the θ axis

m_(y) is the discrete order on the r axis

Ω_(x) is the factor sampling on the θ axis, Ωx≦2π/N_(x)

Ω_(y) is the factor sampling on the r axis, Ωx≦2π/N_(y)

It will be understood that there may be variations of thisrepresentation in various bases of the function, where the coefficientsare used to determine the identification code. The bases may be completeand orthogonal so that the numerical values of the coefficients havephase shift properties that result in a stable Hamming distancecalculation when matching with an identification code from rotated iris.

In some embodiments, the iris code may be stored for later use. Althoughthe iris code may be stored in any suitable manner and in any suitablemedium, in an embodiment the iris code may be stored as part of an irisrecognition enrollment process and may be stored in an iris enrollmentdatabase (e.g., database 90 of system 10, a remote database, and/or anyother suitable database).

At step 64, the iris code associated with the captured iris image may becompared to iris codes stored in an iris enrollment database in order todetermine if there is a match between iris codes. Although this matchingprocess may be performed in any suitable manner, in an embodiment theiris code associated with the captured iris image may be compared toiris codes from the database, and a match determined based on theHamming distance between the two iris codes.

FIG. 9A depicts an exemplary Hamming distance distribution forcomparison of iris codes in accordance with some embodiments of thepresent disclosure. The greater the Hamming distance, the greater thedifference between the two iris codes, and similarly, a smaller Hammingdistance represents a lesser difference between the two iris codes. Aself-matching image produces a Hamming distance of zero. However, thematching process is not perfect, but rather, matching between twoindependent snapshots of the same subject and the same eye will includesome positive residual Hamming distance as a result of noise such asshot noise that is not correlated from one image to the next. Moreover,the fixed pattern noise has poor correlation because of the movement ofthe eye from one image to another when using same camera, and may beuncorrelated if the two images are produced on two different cameras. Inaddition, images from the same eye may produce some small variations onHamming distance with dilatation of the pupil, a different eyelidaperture cropping a part of the iris, blur from motion, and illuminationdifference. As a result of these natural variations, a Hamming distancefor a match is not zero.

Nonetheless, the difference between a match and a rejection is welldefined. As depicted in FIG. 9A, an exemplary Hamming distancedistribution may include two well-defined regions (id and di), such thata threshold (Th) can be selected that provides a very high probabilityof a correct match based on the Hamming distance being less than thethreshold. If the Hamming distance is less than a threshold, a match isdetermined. A typical methodology for comparison of iris codes isdescribed in U.S. Pat. No. 5,291,560, which is incorporated herein byreference.

MTF Enhancement of Normalized Iris Image

In some embodiments relating to processing of iris images, it may bepossible to perform MTF enhancement on the normalized iris image ratherthan the raw iris image. This MTF enhancement may be represented as adirect convolution process operating as a sharpening process on thenormalized iris image. Although it will be understood that MTFenhancement by convolution may be implemented in any suitable manner,including different numerical methods, in an embodiment this process maybe applied using a kernel or applying a multiplicative 2D mask in theFourier domain. This method may provide precision and reliability, as itrespects the linear properties of the 2D convolution process on thewhole image of an identified region of interest. In some implementationssuch as applications where the image must be processed and analyzed inreal-time, this process may consume less computing resources than MTFenhancement of a raw image.

As described above, the normalized iris image is represented in polarcoordinates in FIG. 3. FIG. 10 depicts MTF enhancement of a normalizediris image in accordance with some embodiments of the presentdisclosure. The normalized iris image is a function of θ and r. The θcoordinate is affected by a scale factor in the Cartesian frequencydomain by this non-Euclidian transform. This scale factor in the spatialfrequency domain is the direct inverse value, as follows:

F(θ,r) is the polar function of iris image in polar coordinates;

FT is the Fourier Transform; and

FT(F(θ,r))=Ĝ(U,V)

where U is subject to an inverse linear function of r, as any change indistance dθ is equivalent to a distance in object space of (r. dθ),where dθ is a small variation on θ

Thus, in the spatial frequency domain, the scaling factor betweenfrequencies U in polar coordinates and frequencies f in object space isU=f/r. MTF enhancement of the normalized iris image in polar coordinatesmay therefore follow this progressive change of frequency scale on U.

In an embodiment, MTF enhancement of the normalized iris image in polarcoordinates may be performed with a linear filter. Although it will beunderstood that any suitable filtering process may be used, inembodiments the filtering process may be performed with a kernelfunction or using convolution in the Fourier space.

In an embodiment, convolution in the Fourier space may involvemultiplication with a gain function, having a numerical value dependingon the frequency modulus. The equivalent Optical Transfer Functionenhancement on original raw image isOTF′(u,v,d)=G(u,v,d)OTF(u,v,d)

Referring again to FIG. 10, in an embodiment the polar image may besplit into several bands 50 at different (r) values, each band 50corresponding to an average (r) value. As depicted in FIG. 10, thesebands may partially overlap to prevent transferring edge artifacts inthe final image fusion.

In an embodiment, the sequence of processing by FFT (Fast FourierTransform) may involve 2 separate Nyquist frequencies on θ and r. If theband size is N_(θ)×N_(r), the Nyquist frequency on θ may be N_(θ)/(4πr)and the Nyquist frequency on r may be N_(r)/(2H), where H is the radialheight of the band along r axis. The frequency scale on the FFT of theband may be calibrated according these Nyquist frequencies, such thateach sample element of the FFT of the band has frequency coordinates uin the range [−(N_(θ)−1)/(4πr)−1; N_(θ)/(4πr)] on the θ angularfrequency, and v in range [−(N_(r)−1)/(2H); N_(r)/(2H)] on the r radialfrequency. Each sample may be a complex number describing phase andamplitude. The amplitude may multiplied by the gain function of MTFGain(f) at the frequency f, with f²=u²+v².

The result may be to produce FFT images 47 for each of the bands, theimages having MTF enhancement based on the by multiplication by Gain(f).The FFT images 47 may then be restored to polar coordinates by theinverse FFT transform, resulting in normalized images for each of thebands 50 having enhanced MTF properties. The MTF enhanced band imagesmay then be merged to generate a fused image 49. The edges of the bandsmay contain some edge artifacts as a natural effect of convolution onthe periodic band, in the same manner as would be produced byconvolution repeating the same band function periodically. These edgeartifacts may automatically be cropped from the final merged image, witheach band cropped at its edges in overlapping areas. The result may bethe MTF enhanced normalized iris image in polar coordinates.

In another embodiment, the MTF enhancement of the normalized iris imagemay be performed by a convolution using a kernel. In the same manner asdescribed above, the normalized iris image may be split into bands. Thekernel of convolution on the θ axis is expanded in 1/r to representcorrectly the same size from the original raw image in Cartesiancoordinates. The merger of the convolved and separated bands may beperformed in the same manner as described for the FFT method describedabove, meaning each of resulted image per band are recombined by samemethod at the end.

Iris Code Equalization

As described herein, in some embodiments in which an EDOF optical systemis used, the raw image may be enhanced prior to or after normalization.In other embodiments, it may be desirable to avoid MTF enhancement ofthe EDOF raw image, for example, to reduce the processing time or theprocessing power necessary to perform the MTF enhancement. In anembodiment, system 10 may generate iris code equalization coefficientsthat facilitate the comparison of a stored iris code with an iris codegenerated from an EDOF image that has not been enhanced, whether or notthe stored iris code was originally generated from a system 10 having anEDOF optical system.

Although equalization coefficients may be generated in any suitablemanner, in an embodiment, the equalization coefficients may be generatedbased on the general characteristic of a wavelet as Gabor or Log-Gaborfunctions having a narrow spectrum. FIG. 4B depicts an exemplary plot ofbase wavelet functions for generating an iris code represented as afunction of spatial frequency in accordance with some embodiments of thepresent disclosure. An analysis of the Fourier Transform of each ofthese elementary functions may demonstrate some typical narrowstructures having a peak value and broadness related to the order valuesof [n_(x), n_(y), m_(x), m_(y)]. It may be possible to determineequalization coefficients based on the narrow spectrum in the spatialfrequency domain of each used base function of the identification codemathematical representation.

In an embodiment, an equalization (or amplification) ratio may becalculated based on the integration of the pondered average byintegration over the spatial spectrum. The pondered average is anaffecting weight value proportional to the amplitude of the spatialspectral density at each special frequency when calculating the averageamplification coefficient. The MTF of the captured and normalized EDOFmay have a mainly local variation of 1^(st) order, such that thevariations of the 2^(nd) order are frequently negligible as a result ofthe low variation of MTF slope across the narrow size of the waveletspectrum. In an embodiment, the equalization ratio may be determinedbased on the ratio between enhanced MTF values and raw MTF values at aconsidered special frequency peak, as depicted in FIG. 4C, which depictsan exemplary plot of the base wavelet functions for generating an iriscode modulated by the gain MTF function, as a function of spatialfrequency, in accordance with some embodiments of the presentdisclosure. The MTF properties for an EDOF system (e.g., the ratiobetween the raw and enhanced MTF for an EDOF system) may be systemdependent and may be constants of the system.

FIG. 4D depicts an exemplary plot of a discrete representation ofequalization coefficients associated with the modulated waveletfunctions of FIG. 4C, as a function of spatial frequency, in accordancewith some embodiments of the present disclosure. At each base function amultiplicative equalization coefficient related to the MTF Gain Function(MGF) may be determined. As described above, the MTF properties may besystem dependent. The coefficients for a system may be determined in anysuitable manner, e.g., based on an actual determined ratio for a system,based on estimated parameters, based on calculated parameters, any othersuitable method, or any combination thereof.

Once the equalization coefficients are determined, they may be used inthe matching process. Before equalization, the iris code numericalvalues are a table of numerical values C_(m) _(x) _(,n) _(x) _(,m) _(y)_(,n) _(y)

After equalization, the iris code numerical values are C′_(m) _(x) _(,n)_(x) _(,m) _(y) _(,n) _(y) with C′_(m) _(x) _(,n) _(x) _(,m) _(y) _(,n)_(y) =A_(m) _(x) _(,n) _(x) _(,m) _(y) _(,n) _(y) ·C_(m) _(x) _(,n) _(x)_(,m) _(y) _(,n) _(y) where A_(m) _(x) _(,n) _(x) _(,m) _(y) _(,n) _(y)are the equalization or amplification coefficients on iris code.

An exemplary embodiment for the use of equalization coefficients isillustrated by using the Discrete Gabor Transform as an example.However, it will be understood that this method may be applicable to anyiris code generation algorithm as long as the base of the function iscontrolled and a limited spatial spectral bandwidth is applied for eachbase function. A simplified 1D representation of a Gabor wavelet basefunction is illustrated on FIG. 8A. Two typical Gabor functions waveletcases A and B are represented on FIG. 8A extracted in 1 dimension forsimplicity of the presentation. A and B may have different modulationfrequencies, that are the frequency peak values in the frequency domainF_(A) and F_(B), e.g., as depicted in FIG. 8B. The equalization, gain oramplification factors to apply are determined by the defined gainfunction A_(m) _(x) _(,n) _(x) _(,m) _(y) _(,n) _(y) =Gain(f) withf=F_(A) or f=F_(B) accordingly, as described above. The equalizationcoefficients are multiplied by each respective coefficient of the iriscode (based on by the designed MTF amplification ratio described anddepicted with respect to FIG. 4A), and corresponding to the average orcentral peak spatial frequency of the spectral signature of theassociated iris code function (e.g., as depicted and described withrespect to FIG. 4D).

EDOF Iris Image Processing

FIG. 7 depicts an exemplary organogram representing four paths P1-P4depicting exemplary sequences for biometric identification from imageacquisition to identification, in accordance with some embodiments ofthe present disclosure. In the exemplary embodiment of FIG. 7, the rawimage captured by image sensor 30 has been captured with an EDOF opticalsystem, having extended of field and MTF characteristics as describedherein. FIG. 7 depicts four alternative processing paths for the EDOFraw image. The first path P1 corresponds to the path of FIG. 5B, andincludes the same steps 61-64 for enhancing the EDOF raw image (step61), normalizing the enhanced image (step 62), generating an iris codefor the normalized enhanced image (step 63), and performing a matchbased on the iris code for the normalized enhanced image (step 64). PathP2 differs from path P1 in that MTF enhancement is performed on thenormalized image at step 65, not on the raw image at step 61. Path P3omits MTF enhancement, but performs the remaining steps, as will bedescribed in more detail below. Finally, path P4 omits MTF enhancement,but adds an additional step of equalization (step 66), as will bedescribed in more detail below.

Referring to path P2, in an embodiment the EDOF raw image may benormalized at step 62. MTF enhancement (e.g., convolution as describedherein) may then be performed after normalization of the EDOF raw imageat step 65 of P2, such that MTF enhancement occurs in the space of thenormalized image. Performing MTF enhancement on the normalized image mayrequire significantly less processing power than performing thisprocessing on the full EDOF raw image as required at step 61 of path P1.In an embodiment, the process of applying the convolution method on thereduced space results in a new rectangular table of data having lessthan 10% of volume of data of the raw image source. Path P2 may beapplicable in iris recognition applications where algorithms generatethe rectangular normalized image extracted from annular area of iris,e.g., as described herein.

The geometrical transformation from a polar representation to arectangular representation may produce a non-uniform stitch on theimage, such that the output sampling pitch on an angle θ increases withthe radial distance. The MTF enhancement may be performed on thenormalized image based on an approximation, which may be determined byconsidering the average pitch of the image. The resulting enhanced andnormalized image of path P2 may have similar properties to the enhancedand normalized image of path P1, but may require significantly lessprocessing overhead. Processing may then continue to iris codegeneration (step 63) and matching (step 64) as described above.

Referring to path P3, in an embodiment the EDOF raw image may beprocessed without MTF enhancement. In an embodiment, the depth of fieldenhancement produced by the spherical aberration of the EDOF opticalsystem may remain active by preventing zeroes and contrast inversion ofthe optical MTF within the extended depth of field. The sphericalaberration may reduce the amplitude of the signal and affect the ratioof amplitude between low and higher spatial frequencies, for example, asshown on FIGS. 6A and 6B. This ratio variation may be progressive withthe spatial frequency without introducing any phase shift in the spatialfrequency or Fourier domain between frequencies. Without theintroduction of the phase shift, this may limit the production ofartifacts from the image space that could affect directly the matchingprocess when calculating the Hamming distance (e.g., by increasingrandomly the Hamming distance). As a result, there is a low dispersionon the Hamming distance, which may limit the error rate, even withoutMTF enhancement. In an embodiment, the error rate may be reduced byusing functions for the Hamming distance calculation that have adominant weight on low spatial frequencies (“LSF”), e.g., thefrequencies depicted in FIG. 6B. The dispersion effect will increase,however, to the degree that the medium spatial frequency (“MSF”) andhigh spatial frequency (“HSF”) are used. On the normalized image space,this regular and continuous increase of MTF ratio between enhanced andnon-enhanced MTF may prevent generation of artifacts that could affectthe Hamming distance when matching.

In an embodiment, the imaging system used for enrollment in the irisdatabase may have similar optical characteristics (e.g., an EDOF opticalsystem having spherical aberration). Using a similar system forenrollment (with or without MTF enhancement) and capture may result in alower error rate. Whatever system is used for enrollment, path P3 maymaintain compatibility with existing iris databases (e.g., ISO INCITS379 and ISO 19794-6).

Referring to path P4, in an embodiment the EDOF raw image may beprocessed without MTF enhancement, but with an added equalization step66. As described above, the equalization process may result in animprovement in the comparison of an iris code from an image that has notundergone MTF enhancement with an image from an iris enrollmentdatabase, resulting in a reduction of the Hamming distance that wouldexist without equalization. The raw EDOF iris image is normalized atstep 62, an iris code is generated for the normalized image at step 63,equalization is performed at step 66, and the iris codes are compared atstep 64.

FIG. 9B depicts exemplary Hamming distance distributions for comparisonof iris codes based on different iris enrollment and capture proceduresin accordance with some embodiments of the present disclosure. The plotEq1 may represent the statistical histogram of the Hamming distanceproduced by matching the same eye where the captured and stored image ofthe same iris were both produced with a lens lacking sphericalaberration, where one image was captured with a lens lacking sphericalaberration and the other image was captured by a lens having controlledspherical aberration and a system employing an enhanced MTF technique,or where both images were produced by a lens having controlled sphericalaberration and a system employing an enhanced MTF technique. The plotEq2 may represent the statistical histogram of the Hamming distanceproduced by matching the same eye with lenses both having controlledamount of spherical aberration but without MTF enhancement. Because theMTF is lower by adding spherical aberration, the signal to noise ratiomay increase while no information is lost. The effect of relativelyhigher noise slightly enlarges the Hamming distance dispersion andproduces a slight increase of error probability. The plot Eq3 mayrepresent the statistical histogram of the Hamming distance produced bymatching the same eye where one of the two images is produced with alens lacking spherical aberration or with a lens having controlledspherical aberration and a system having MTF enhancement, and the otherimage is produced with a lens having controlled spherical aberration andno MTF enhancement. Because the MTF ratio of the two images is notconstant with the spatial frequency, this may produce some slightadditional distortion between the coefficients of the iris code and thusenlarge the dispersion of Hamming distance.

The plots Df1, Df2 and Df3 are respectively the Hamming distances ofmatching different eyes from different subjects, with capture andenrollment systems configured as described above for Eq1, Eq2, and Eq3.Although not depicted in FIG. 9B, the statistical plots Eq2, Eq3, Df2,and Df3 may have dispersion characteristics that are closer to Eq1 andDf1 when the identification algorithms are using mainly information fromlow spatial frequencies, based on the MTF characteristics for lowspatial frequencies as described above with respect to FIG. 6B. In thismanner, the relative amplitude of the coding coefficients is affectedwhile maintaining strong correlation between the coefficients, such thatthe calculation of the Hamming distance is not significantly affected.As depicted in FIG. 9B, a threshold distance Th may be selected thatresults in a highly accurate determination of iris code matches,whichever optical system or processing path is used as described above.

The foregoing is merely illustrative of the principles of thisdisclosure and various modifications may be made by those skilled in theart without departing from the scope of this disclosure. The abovedescribed embodiments are presented for purposes of illustration and notof limitation. The present disclosure also can take many forms otherthan those explicitly described herein. Accordingly, it is emphasizedthat this disclosure is not limited to the explicitly disclosed methods,systems, and apparatuses, but is intended to include variations to andmodifications thereof, which are within the spirit of the followingclaims.

As a further example, variations of apparatus or process parameters(e.g., dimensions, configurations, components, process step order, etc.)may be made to further optimize the provided structures, devices andmethods, as shown and described herein. In any event, the structures anddevices, as well as the associated methods, described herein have manyapplications. Therefore, the disclosed subject matter should not belimited to any single embodiment described herein, but rather should beconstrued in breadth and scope in accordance with the appended claims.

What is claimed is:
 1. A method of processing an extended depth-of-field(EDOF) image of an iris at an imaging wavelength λ_(IM), comprising:capturing a raw image of the iris, wherein the raw image has a reducedmodulation transfer function (MTF) based on an optical system having anamount of spherical aberration (SA) of 0.2λ_(IM)≦SA≦2λ_(IM); normalizingthe raw image; and generating an iris code based on the normalized rawimage, comprising performing an MTF enhancement of the normalized rawimage in polar coordinates to generate a MTF enhanced image, comprising:selecting a plurality of bands from the normalized raw image; processingeach of the bands to enhance the MTF; and fusing the bands to generatethe MTF enhanced image; and generating the iris code from the MTFenhanced image.
 2. The method of claim 1, further comprising storing theMTF enhanced image in an iris enrollment database.
 3. The method ofclaim 1, wherein processing each of the bands to enhance the MTFcomprises processing each band with a fast Fourier transform.
 4. Themethod of claim 1, wherein processing each of the bands to enhance theMTF comprised processing each band with a kernel.
 5. A method ofprocessing an extended depth-of-field (EDOF) image of an iris at animaging wavelength λ_(IM), comprising: capturing a raw image of theiris, wherein the raw image has a reduced modulation transfer function(MTF) based on an optical system having an amount of sphericalaberration (SA) of 0.2λ_(IM)≦SA≦2λ_(IM); normalizing the raw image;generating an iris code based on the normalized raw image, whereingenerating an iris code based on the normalized raw image comprisesgenerating the iris code directly from the normalized raw image; andgenerating an equalized iris code based on the iris code and iris codeequalization coefficients; wherein the iris code equalizationcoefficients have a base function covering a range of spatial frequencybands with related coefficients amplified according to a determinedoutput MTF at related spatial frequencies.
 6. The method of claim 1,further comprising storing the raw image in an iris enrollment database.7. The method of claim 1, further comprising storing the normalized rawimage in an iris enrollment database.
 8. The method of claim 1, furthercomprising storing the iris code in an iris enrollment database.
 9. Themethod of claim 1, further comprising comparing the iris code to one ormore known iris codes.
 10. The method of claim 9, wherein the known iriscodes were originally obtained by an optical system having no enhanceddepth of field function.
 11. The method of claim 9, wherein the knowniris codes were originally obtained by an optical system having anenhanced depth of field function without MTF enhancement.
 12. The methodof claim 1, wherein the optical system comprises a single lens system.13. The method of claim 12, wherein an aperture stop for the opticalsystem is located at a position that minimizes comatic aberration. 14.The method of claim 12, wherein the single lens comprises glass orplastic.
 15. The method of claim 12, wherein the single lens comprises arotationally symmetric optical component.
 16. The system of claim 12,wherein the single lens comprises a spherical refractive surface.
 17. Asystem for processing an extended depth-of-field (EDOF) image of an irisat an imaging wavelength λ_(IM), comprising: an optical system having anamount of spherical aberration (SA) of 0.2λ_(IM)≦SA≦2λ_(IM), the opticalsystem being configured to form on an image sensor a raw image havingreduced a modulation transfer function (MTF) based on the sphericalaberration; a controller electrically connected to the image sensor,wherein the controller is configured to capture a raw image of the iris,normalize the raw image, and generate an iris code based on thenormalized raw image, wherein the controller is configured to perform anMTF enhancement of the normalized raw image in polar coordinates togenerate a MTF enhanced image, and generate the iris code from the MTFenhanced image, and wherein the controller is configured to select aplurality of bands from the normalized raw image, process each of thebands to enhance the MTF, and fuse the bands to generate the MTFenhanced image.
 18. The system of claim 17, further comprising an irisenrollment database, wherein the controller is configured to transmitthe MTF enhanced image to the iris enrollment database.
 19. The systemof claim 17, wherein the controller is configured to utilize a fastFourier transform to process each of the bands to enhance the MTF. 20.The system of claim 17, wherein the controller is configured to utilizea kernel to process each of the bands to enhance the MTF.
 21. A systemfor processing an extended depth-of-field (EDOF) image of an iris at animaging wavelength λ_(IM), comprising: an optical system having anamount of spherical aberration (SA) of 0.2λ_(IM)≦SA≦2λ_(IM), the opticalsystem being configured to form on an image sensor a raw image havingreduced a modulation transfer function (MTF) based on the sphericalaberration; a controller electrically connected to the image sensor,wherein the controller is configured to capture a raw image of the iris,normalize the raw image, and generate an iris code based on thenormalized raw image, wherein the controller is configured to generatethe iris code directly from the normalized raw image, wherein thecontroller is further configured to generate an equalized iris codebased on the iris code and iris code equalization coefficients, andwherein the iris code equalization coefficients have a base functioncovering a range of spatial frequency bands with related coefficientsamplified according to a determined output MTF at related spatialfrequencies.
 22. The system of claim 17, further comprising an irisenrollment database, wherein the controller is configured to transmitthe raw image to the iris enrollment database.
 23. The system of claim17, further comprising an iris enrollment database, wherein thecontroller is configured to transmit the normalized raw image to theiris enrollment database.
 24. The system of claim 17, further comprisingan iris enrollment database, wherein the controller is configured totransmit the iris code to the iris enrollment database.
 25. The systemof claim 17, wherein the controller is further configured to compare theiris code to one or more known iris codes.
 26. The system of claim 25,wherein the known iris codes were originally obtained by an opticalsystem having no enhanced depth of field function.
 27. The system ofclaim 25, wherein the known iris codes were originally obtained by anoptical system having an enhanced depth of field function without MTFenhancement.
 28. The system of claim 17, wherein the optical systemcomprises a single lens system.
 29. The system of claim 28, wherein anaperture stop for the optical system is located at a position thatminimizes comatic aberration.
 30. The system of claim 28, wherein thesingle lens comprises glass or plastic.
 31. The system of claim 28,wherein the single lens comprises a rotationally symmetric opticalcomponent.
 32. The system of claim 28, wherein the single lens comprisesa spherical refractive surface.
 33. The method of claim 5, furthercomprising storing the raw image in an iris enrollment database.
 34. Themethod of claim 5, further comprising storing the normalized raw imagein an iris enrollment database.
 35. The method of claim 5, furthercomprising storing the iris code in an iris enrollment database.
 36. Themethod of claim 5, further comprising comparing the iris code to one ormore known iris codes.
 37. The method of claim 36, wherein the knowniris codes were originally obtained by an optical system having noenhanced depth of field function.
 38. The method of claim 36, herein theknown iris codes were originally obtained by an optical system having anenhanced depth of field function without MTF enhancement.
 39. The methodof claim 5, wherein the optical system comprises a single lens system.40. The method of claim 39, wherein an aperture stop for the opticalsystem is located at a position that minimizes comatic aberration. 41.The method of claim 39, wherein the single lens comprises glass orplastic.
 42. The method of claim 39, wherein the single lens comprises arotationally symmetric optical component.
 43. The method of claim 39,wherein the single lens comprises a spherical refractive surface. 44.The system of claim 21, further comprising an iris enrollment database,wherein the controller is configured to transmit the raw image to theiris enrollment database.
 45. The system of claim 21, further comprisingan iris enrollment database, wherein the controller is configured totransmit the normalized raw image to the iris enrollment database. 46.The system of claim 21, further comprising an iris enrollment database,wherein the controller is configured to transmit the iris code to theiris enrollment database.
 47. The system of claim 21, wherein thecontroller is further configured to compare the iris code to one or moreknown iris codes.
 48. The system of claim 47, wherein the known iriscodes were originally obtained by an optical system having no enhanceddepth of field function.
 49. The system of claim 47, wherein the knowniris codes were originally obtained by an optical system having anenhanced depth of field function without MTF enhancement.
 50. The systemof claim 21, wherein the optical system comprises a single lens system.51. The system of claim 50, wherein an aperture stop for the opticalsystem is located at a position that minimizes comatic aberration. 52.The system of claim 50, wherein the single lens comprises glass orplastic.
 53. The system of claim 50, wherein the single lens comprises arotationally symmetric optical component.
 54. The system of claim 50,wherein the single lens comprises a spherical refractive surface.